From a computation theoretic perspective, pre-processing and post-processing function design problems of AirComp systems for different fusion functions have been comprehensively investigated in [1]}, [2]}, [3]}.
From a wireless communications perspective,
due to the imperfection of practical MAC with non-zero
receiver noise, unequal channel coefficients and limited transmit power budgets, the output signal of a MAC is not a perfect sum of the pre-processed sensor signals as expected.
Thus, most recent work focuses on optimal AirComp transmitter and receiver policy design for achieving the minimum computation mean-squared error (MSE) of the sum of pre-processed signals [4]}, [5]}, [6]}, [7]}.
In [4]}, the computation MSE of the sum signal under imperfect channel state information was investigated.
In [5]},
the optimal single-antenna AirComp design and the scaling law analysis of computation MSE and transmit power consumption were derived in terms of the number of sensors.
In [6]} and [7]}, the transmitting and receiving beamforming of multi-antenna AirComp systems were considered to minimize the computation MSE.
In particular, AirComp has been applied to emerging wireless applications such as wireless distributed machine learning [12]}, and over-the-air consensus [13]}.
